Calculating useful indicators of EBFM

Preface

Acknowledgements

This code is based on code by Joanne Potts and the original R-Markdown document written by Linda Thomas, Camilla Novaglio, Beth Fulton & Javier Porobic, “Lenfest model indicators - calculation for EwE models”, dated 19/07/2021.

Coding notes

This code is written in Quarto, which enables you to weave together content and executable code into a finished document. To learn more about Quarto see https://quarto.org.

By default, all code echoing is switched to false to ensure the produced html document is easy to read, including output only not all the code steps. Change echo: true in the YAML (box at the top of the qmd file) if you want to see more information.

Render the Document

to create a html file that includes all of the steps and output click the Render button (blue arrow in the menu bar at the top of the quarto code window). This html document will include both text content and the output of embedded code.

Running Code

If you want to execute the code manually - block by block - run the blocks sequentially. To execute a block of code click the small green arrow in the top right of that block. Many blocks create output files (images of plots). When you reach the end of the blocks, to get the html document you will still need to Render the file.

Step 1 - Set up

Set the File paths - Please enter the following information:

Directory where the ID and consumption csv files are stored and
Directory where Ecosim output is stored
Directory where you desire the output of this quarto R file

Specify files names

Specify analysis parameters - settings required to run all the following code steps for your system

Import the functions needed to run the code

Load the relevant libraries and initialise the output directories

Set graphics parameters

Step 1 - Finding Hub species

Undertake the steps to calculate the hub species

Determine the Hub species

<environment: R_GlobalEnv>

List the Hub species. Check they make sense for your system - they should be prey species consumed by many species in the system or predators that link across the top of the food web, consuming prey from many sub-webs.

[1] "Demersal sharks"  "Whiting"          "ShSmInvertFeeder" "ShSmPredator"    
[5] "Mesopelagics"     "Squid"            "Macrobenthos"     "Megabenthos"

Step 2 - Load the data from Ecosim

Import all the data required to calculate the indicators

<environment: R_GlobalEnv>

Step 3 - Run diagnostics

Create time series plots of the input time series (from Ecosim) . This helps check everything is as it should be in the “input data” coming from Ecosim. It will also help with interpretation of the final indicator results

Also run multivariate analysis - PCA of catch through time so you can see which years resemble each other and whether there have been major changes in catch composition (another reality check point)

Step 4 - Calculate EBFM indicators

Calculate system status indicators that have repeatedly been found to be useful in EBFM contexts:

Exploitation rate: catch/biomass
Inverse of exploitation rate at the system level - 1/(biomass/landings)
Biomass ratio - piscivorous:zooplanktivorous fish
Biomass ratio - pelagic:demersal fish
Coefficient of variation of ecosystem (t) versus individual (i)
Mean length in a community or catch- Assumes Linf is in Species_ID.csv file
Mean trophic level of community, catch - Trophic level calculated by EwE model based on diet (not biomass).
Mean longevity - Assumes MaxAge is in Species_ID.csv file
Proportion of large fish (LFI) - based on Linf in Species_ID.csv file
Ryther - catch per unit area (divide total catch by area of the model to get this value)
Fogarty - total catch / total primary production (units are per mil - o/oo where 0.001 is 1 o/oo)
Friedland - use catch: Chlorophyll a (basically doing Fogarty but use Chl a instead if primary production is not available. For EwE calcaulte off primary production but also plot it up based on assuptions of biomass:C -> c: Chla -> final calculations
Cumulative biomass (survey or catch) vs Trophic level – steepness of the curve and height of the asymptote are indicators of overall system state

NOAA’s Exploitation status- FSSI. The FSSI method looks at B vs Blim (to see if overfished). The FSSI method also looks at B vs Btarg. Both of these bits of information is also used in the calculation of the ETI below. Finally the FSSI method looks at F vs Ftarg (to see if overfishing). The method count the number of species in each state.

Calculate system structure indicators:

Greenband index - whether disproportionate pressure is being put on ecosystem structure. Checks to see if the pattern of fishing mortality across species matches the predation profile in an unfished system. Ideally species sit within the Greenband (the profiles match). If they are above then there is excessive pressure on that part of the food web. If species sit below the greenband there is the potential for the expansion of exploitation on those species
Gao index: how resilient the food web structure is based on the number of trophic linkages and the flow through the different potential sub-webs.
Ecosystem Traits Index (ETI) - which uses the status of groups in the different classes (classes = Classification from species_ID.csv) and the resilience of the overall structure to give an index of ecosystem health. This is a 10 point scale.

<environment: R_GlobalEnv>

Glossary of terms

Criticality analysis – analysis of network structure to identify nodes or segments (nodes and links) that are critical to performance of the network. The flow through the network would severely degrade If these critical components are lost, leading to the failure or fragmentation of the network.

Degree – The number of connections (in or out) of a node in a network.

Degree in – The number of connections into a node in a network.

Degree out – The number of connections out of a node in a network.

Ecological (functional) traits – characteristics of species (morphological, physiological, or phenological) that influences the ecological processes of a species, how it responds to environmental pressures and its role in the structure and function of an ecosystem.

Ecological integrity – the capacity of an ecosystem to support and maintain ecological processes and biodiversity (content and structure).

Ecosystem structure – the network of biotic and abiotic components making up an ecosystem (note in this paper we focus only on the biotic and infer continuance of abiotic connections).

Ecosystem function – the combined set of ecological processes controlling the flux of matter (including nutrients) and energy through an ecosystem.

Ecosystem health – capacity of the ecosystem to maintain structure and function on ecological and evolutionary time scales.

Functional diversity – the diversity of functional traits (from across the components of an ecosystem) that influence function of an ecosystem (across ecological and evolutionary time scales).

Functional groups – group of species sharing common characteristics (traits such as size, longevity, diet, habitat use) and have a similar role in an ecosystem.

Gao index – a scalar defined based on the position of an ecosystem in a space defined by Network heterogeneity and Network density. If the point representing the ecosystem sits in the area below the collapse horizon (see the main text for the description of how to calculate this transition surface) then it receives the lowest possible score for this semi-quantitative index (0.5 in this application). If it sits in the quadrant defined as being above the point of intersection of the collapse horizon and the x and y axes of the space then the system receives the highest possible score (1). If the point is above one of the intercepts but not both (i.e. is above the collapse horizon but not in the fully resilient quadrant) then it receives an intermediate score (0.8 in this application).

Green Band – an acceptable band of exploitation pressure that does not put distortive pressure on ecosystem structure, as it matches the biomass-production profile of the unfished/unperturbed state of that ecosystem. If the human induced mortality for those species-groups (e.g. as represented by catch volume) sees them sit within the band they are being fished in a “structurally sustainable” way. If their point sits below the Green Band there is potential to increase the mortality/extraction without imposing structurally distortive pressure via that species group. If the point sits above the Green Band then “structural overfishing” is occurring and pressure should be reduced.

Hub index – minimum of the rank (lowest numerical value) of a species group based on the network indices of degree, degree out and pagerank. Ranks begin at 1 (the highest rank) for the species group with the highest score for that network index and increase to n (where n is the total number of species groups in the network) for the species group with the lowest value of that index. The species with 5% of species groups in the ecosystem with the lowest hub index (effectively the most highly ranked species) are identified as hub species.

Hub species – highly connected species (nodes in the network) that are found to tie the system together structurally and to facilitate trophic flow across a broad part of the system. The loss of these species would lead to bottlenecks or splinter the network degrading its function.

Node – species in an ecological network (or functional groups in less resolved ecological networks), where connections between the nodes may be due to habitat dependency or feeding interactions.

Network density – how many connections a network has versus the total possible. While in some usage it is a normalised value, here it is implemented as the average weighted degree.

Network heterogeneity – a measure of how variable flows are across the network (calculated here based on the variance in the weighted connections in the network).

Network motif – these patterns of interconnections found in complex networks are in effect the structural representation of processes such as predation or competition, as they are defined through the ways nodes interact (directly and indirectly).

Network symmetry – the in–out weighted-degree correlation coefficient (i.e. whether a node with a high inflow has a high outflow).

Pagerank – This index is a variant of the eigenvector centrality concept and is used by companies, such as Google, to rate the importance of websites (to improve search efficiency and web maintenance prioritisation). The index involves counting the number and quality/strength (weight) of links to a node - more important nodes are cross linked with and support more nodes. We use energy flow through the system, as represented by consumption, as the link weights used to calculate this index.

Responsiveness – whether an indicator reflects change quickly.

Sensitivity – whether an indicator provides a clear and interpretable signal of real change.

Specificity – whether an indicator responds only to change due to a specific stressor.

Structural resilience – the capacity of the network structure to continue functioning without degradation when nodes in the system are perturbed.

Symmetry – see network symmetry above.

Topology – how the ecosystem is structured, what is connected to what, and which aspects (connections, species or functional groups) are most important to its ecological integrity.

Tables Used in the Calculation of the Structural Indicators

Table 1: The ETI Qualitative Rating system. The break points used in the qualitative rating are roughly regular (with a small deviation in the Shocks likely band, which is slightly broader than other bands) to avoid any strong non-linearities in the rating system. In contrast, the breakpoints the simple qualitative “Management Guidance” bands is nonlinear and is based on the dynamic responses seen in the simulated ecosystems as they transitioned through the different ETI values.

ETI value	Qualitative Rating	Colour	Management Guidance
< 2.5	Collapse likely	Dark red	Urgent Intervention: Degraded structure and function
2.5 – 3.7	Shocks likely	Bright red	Requires immediate large-scale action; likely to take considerable time to recover
3.7 – 4.6	Shocks possible	Dark Orange	Act: At risk
4.6 – 5.5	Low integrity	Orange	Requires attention; should respond rapidly to intervention
5.5 – 6.4	Medium integrity	Dark yellow	Monitor: Still stable
6.4 – 7.3	Medium-High integrity	Yellow	Continue monitoring; no changes required
7.3 – 8.2	High integrity	Light green	Stable: Not at risk
8.2 – 9.1	Very robust integrity	Green	Continue monitoring; potential for increased activity (exploitation)
9.1 – 10	Close to pristine	Dark green
> 10	Pristine	Very dark green

Supporting information - tables of logic used during calculation of the structural indicators

Table 2: Species classification scheme.

Classification	Description	Target relative biomass levels (vs B_unfished)	Weight
Vulnerable	Slow growing, late maturing species susceptible to fishing pressure (such as marine mammals, seabirds and large sharks)	0.5-0.7	1
Habitat	Biogenic habitat forming species	0.3-0.6	1
Target	Primary target species of a fishery	0.4-0.5	0.5
Byproduct	These species have some value and are landed by fisheries but are not the main targeted species	0.35-0.4	1
Bycatch	Species that are not retained by the fishery	0.2-0.4	0.1
Robust	Fast growing, short lived species (such as productive invertebrates like cephalopods or microfauna like zooplankton)	0.4-0.5	0.1
Hub	Species identified as being a hub species using the degree and PageRank scores.	0.6-0.7	1

Table 3: Qualitative scoring schemes for position relative to the Green Band and for relative biomass. Default target biomass levels are given in Table S1.

Green Band scoring system		Relative biomass scoring scheme
Fail: Above Green Band		Fail: below target band
Acceptable: In Green Band		Acceptable: within target band
Light: Below Green Band		Light: above target band

Table 4: Matrix of possible combinations of fail (F), light (L) and acceptable (A) values of the Green Band (GB) and relative biomass (RelB) and the associated “combination score” (k for use in equation 4), for different categories of species.

GB-RelB	Vulnerable	Habitat	Target	Byproduct	Bycatch	Robust	Hub	k^*
F-F								0
F-A								0.25
F-L								0.5
A-F								0.375
A-A								1
A-L								1.5
L-F								0.75
L-A								2
L-L								2.5

* Note there is an intentional asymmetry in the values (so a F-A gets a lower value than a A-F), this is because removing distortive pressure is more immediately important than the relative biomass (which can be environmentally influenced by interannual variation); acting to remove pressure will also benefit relative biomass in the longer term.